Environmental Regulations and Carbon Emissions: The Role of Renewable Energy Research and Development Expenditures

Abstract

This present research offers fresh insights regarding the causality nexus between environmental regulations and a sustainable environment. Also, this study considered the importance of renewable energy research and development (RERD), technological innovation (TI), and economic growth (GDP). Using the U.S. extended dataset covering the period 1990–2020; this research employed the wavelet methods (wavelet power spectrum and wavelet coherence) to observe the causal connections between mentioned variables based on the time-frequency domain. The empirical results from the wavelet power spectrum asserted that carbon emissions (CO₂), RERD, and TI are vulnerable during the study period, while GDP and environmental policies are stable. Additionally, the wavelet coherence approach unveils relationships both in-phase and anti-phase. A causal connection is evident between CO₂ and other variables. Particularly, a unidirectional causality is found from TI to CO₂ emissions, while a bidirectional causal association exists between GDP and CO₂, and environmental policy stringency, and CO₂. Moreover, a bidirectional causality exists between RERD and CO₂, but this association is insignificant. Based on findings, this research suggests enhancing RERD investment, strengthening environmental regulations, and promoting green technological innovation to attain a sustainable environment.

1. Introduction

Environmental degradation has become one of the biggest problems facing humanity, threatening human health and economic development [1]. IPCC (Intergovernmental Panel on Climate Change) has warned that we may face “serious environmental challenges” sooner than expected due to increasing emissions [2]. Despite this stern warning, the climate crisis continues to persist as the international organizations avoid the whole undertaking needed for its recovery. Even the United Nations points out that “climate change will have even more devastating consequences than the current COVID-19 pandemic if the global community does not act immediately and decisively”. Some climate calamities are caused by the growing threat of global warming, with 2019 set to be the second-hottest year on record [3].

The United Nations [4] calls for limiting global warming to 1.5 degrees Celsius, but with contributions now being made at the national level [3], the world is well on its way to missing that target. Due to pressure for rapid economic growth and the resulting problem of increasing atmospheric CO₂ emissions driving climate change and global warming, energy consumption has increased. More than two-thirds of all greenhouse gas emissions come from the energy industry, which accounts for about 80% of CO₂ emissions [5]. CO₂ is believed to be the main cause of climate change and global warming. According to Leaver [5], there has been a significant increase in CO₂ emissions from energy-related sources: from 20,521 Mt (million tonnes) in 1990 to about 32,840 Mt in 2017.

To reduce the negative impacts of all these major risks of climate change and global warming, sound energy policies and regulatory frameworks are needed. Strict environmental regulations are fast becoming the principles of sustainable development and a means to reduce CO₂ emissions, as people have become aware of these serious threats and realized that market forces alone cannot solve environmental problems [6]. However, this policy instrument is only one of several available alternatives to reduce climate change and the unfavorable effects of global warming. We also know that this policy instrument cannot minimize the adverse effects of CO₂. According to the OECD, there are over 3200 environmental instruments, with over 2800 in force. A widely recognized policy instrument for reducing CO₂ is the carbon tax, also known as the Emissions Trading Scheme (ETS). It has been charging for the emission of CO₂, which is widely recognized as the most effective approach to reduce emissions [7]. This study emphasizes environmental policy stringency, which could be a corrective strategy to solve the aforementioned problems, while previous studies focused more on environmental- or emission-related taxes.

The essential step to diminish CO₂ emissions caused by fossil fuels and to ensure sustainable economic growth is to enhance the usage of renewables [8]. Consequently, increasing the share of renewable energy in the overall energy mix is crucial for a sustainable and balanced energy economy. However, to achieve the share of renewable energy for environmental recovery, huge investments in renewable energy research and development (R&D) are required. Renewable energy holds importance in attaining environmental sustainability [9]. However, the existing literature mainly focuses on renewable energy consumption. Therefore, current research emphasizes the importance of renewable energy related R&D (RERD) for environmental sustainability.

The influence of environmental regulations on the quality of the environment has already been the subject of several researches [10,11,12,13]. The main objective of this study is to empirically investigate the causal nexus between environmental regulations and a sustainable environment, which could better be captured with environmental policy stringency and CO₂. This research also investigates the role or causal association between RERD and a sustainable environment. Most previous studies addressed the impact of total R&D expenditures on environmental quality. However, RERD, an important environmental indicator, has been less explored [14,15,16,17,18,19]. Finally, this paper analyzes the causal correlation of economic expansion and technological innovation (TI) with the sustainable environment. Earlier studies have analytically investigated the importance of these variables for environmental sustainability. However, the causal association is blurred and needs further research. To achieve the objectives, this research implemented the novel wavelet approach, one of the best approaches for investigating the causal relationships between time series.

Subsequent sections of the manuscript are organized as follows: Section 2 of the paper provides a comprehensive literature review covering all relevant research variables. This is followed by Section 3, which describes the data and methods used in the study. Section 4 presents the results and discussion, while Section 5 formulates conclusions and policy suggestions in line with the research findings.

2. Literature Review

Yang et al. [20] looked into 24 separate economies across the Silk Road Economic Belt (SREB) from 1995 to 2014 based on previous studies. The environmental Kuznets curve (EKC) paradox is confirmed by the research’s use of the ARDL model and for the study region. The study also discovered that increased capital development and the use of renewable energy (RE) both support environmental sustainability. In a similar line, Wen et al. [18] analyzed the South Asian region between 1985 and 2018 by employing the FMOLS approach and establishing the validity of the EKC hypothesis. In the first stage, increased economic expansion leads to increased environmental degradation. However, reaching a certain income level then harms environmental deterioration. Song [16] utilized a fixed-effect threshold regression model on data from 2001 to 2016 in research on 30 Chinese provinces. According to empirical estimations, regional economic growth is boosted by high-level continuous investments in technology and environmental protection initiatives. The report showed that the country could become carbon neutral by investing in and developing the renewable energy industry and its energy distribution system. The literature has long stressed how seriously the environment is impacted by economic growth. To determine the causality association between economic expansion and CO₂, the study by Zhang et al. [21] examined China from 1965 to 2019. The empirical results of the Granger causality assessment reveal just one causal association between the two runs from economic development to CO₂. The study concludes that enhancement in economic expansion may be a factor in CO₂. At the same time, no causality was detected between CO₂ and economic expansion.

By using the CCEMG and AMG techniques, Li et al. [22] examined economic expansion, energy usage, and CO₂ for the period of 1992–2014 for the G20 economies. The projected results asserted that CO₂ levels in the area are considerably influenced by both economic growth and energy usage. The analysis also conclusively shows a bidirectional causal relationship between economic expansion and CO₂. The ARDL technique was used on the data for the 1965–2015 period in the instance of Pakistan for the same relationship. In the short as well as long term, the estimated results support the findings of Li et al. [22]. Studies have shown that economic expansion and energy use are the main reasons for CO₂ [16,18,21]. However, Yang et al. [23] maintained that emerging nations like China could achieve their CO₂ reduction and economic growth goals. To achieve more economic growth, it is important to enhance fixed capital, human capital, fossil, and non-fossil fuel energy. At the same time, reduced fossil fuel energy and the former factors lead to achieving the CO₂ reduction target. Moreover, the global decoupling state of economic growth from CO₂ has changed from a weak to a strong decoupling state from 2000 to 2017 [24]. Studies suggested that energy-saving technological progress, efficiency in production, renewable energy, high oil prices, green financial development, human capital development, trade openness, globalization, and financial inclusion are the factors that may assist economic development decoupling from CO₂ [17,24,25,26].

To achieve environmental sustainability, countries across the globe have taken numerous steps, where stringent environmental policy is among the prime focuses of scholars and policymakers. Numerous pieces of empirical evidence have been reported in the studies concerning the correlation between environmental policies and environmental quality. Specifically, Sohag et al. [27] investigated 77 regions of the Russian Federation throughout 1999–2015 and employed dynamic threshold regression. Empirical outcomes of the study unveiled that gross regional product is a substantial factor of EKC hypothesis validation in the region, whereas TI explains the declining portion of the EKC hypothesis. In addition, environmental policy stringency significantly reduces CO₂ in the area. In contrast, Wolde-Rufael and Weldemeskel [19] and Wolde-Rufael and Mulat-Weldemeskel [28] discovered an inverted U-shaped association between stringent environmental policy and CO₂. This indicates that firstly, stringent environmental policies do not enhance environmental quality but negatively affect environmental problems after reaching a threshold level. Moreover, environmental taxes are found to have a significant adverse impact on CO₂. Additionally, the study additionally argued a one-way causal association running from stringent environmental policy and environmental taxes to CO₂. In the same vein, Shahzad et al. [29] and Godawska and Wyrobek [14] also support the stance that environmental policies and regulations and income significantly promote renewable energy generation, which consequently reduces environmental degradation and helps achieve sustainable development goals (SDG-7). Similarly, Kongbuamai et al. [30] empirically investigated BRICS economies over 1995–2016 and employed dynamic, seemingly unrelated regression and causality tests. The empirical results revealed that economic development, renewable and non-renewable energy consumption positively affect ecological footprints. Conversely, environmental policy stringency negatively and significantly affects ecological footprints with a unidirectional causality from ecological footprint to environmental policy stringency. Moreover, Albulescu et al. [31] offer evidence concerning the negative influence of environmental policy stringency on CO₂, but the impact is found more powerful with a lower level of CO₂.

Additionally, most countries across the globe and particularly developed nations, have speeded up their actions against environmental degradation. In this sense, academics and decision-makers rely heavily on fostering R&D investment and technical innovation. There is a wealth of literature on the impact of R&D and TI. The FMOLS technique was specifically used by Wang and Zhang [17] to examine the BRICS economies from 1996 to 2014. The analysis findings showed that a rise in R&D spending considerably lowers CO₂ in the area. The study concludes that R&D spending may be key in uncoupling economic growth from CO₂. In addition to general R&D, RERD might contribute significantly to establish a low-carbon economy. Shao et al. [15] investigated the U.S. economy covering the period 1990–2019. The study used dynamic OLS and FMOLS to assert that RERD positively and significantly contributes to carbon neutrality target achievement. Moreover, the research also confirms a reciprocal causal relationship between research and RERD and CO₂. Examining 25 EU countries throughout 1998–2014, Paramati et al. [8] confirmed that R&D growth significantly promotes renewable energy consumption, reducing environmental degradation. In addition, Adedoyin et al. [32], Adedoyin et al. [33], and Ullah et al. [12] also support the findings that R&D is playing a positive role in attaining a low-carbon economy, while Wang and Wang [34] conclude its role in decoupling economic development from CO₂.

Furthermore, regarding TI, Zhang et al. [13] investigated the impact of industrial structure and TI on CO₂ in 281 Chinese cities. Empirical results asserted that technological progress and efficiency improvement significantly reduces CO₂ intensity. The research work of Lyu et al. [11] used different methods to analyze the impact of CO₂ trading systems on TI. The study concludes that the CO₂ trading system significantly enhances low carbon TI only in the short run. In the case of Pakistan, Ullah et al. [12] investigated data from 1990 to 2018 and utilized the ARDL approach. The examined results unveil that TI’s positive and negative shocks exhibit mixed (symmetric and asymmetric) impacts on CO₂. Moreover, Cheng et al. [10] reveal that RE’s TI significantly helps reduction in CO₂ levels while fossil fuel TI significantly enhances CO₂ in China. Although these studies have mentioned the positive impact of TI on CO₂ reduction, Razzaq et al. [35] used the quantile ARDL approach in China and concluded an insignificant impact of TI on CO₂. However, it validates the previous findings in the long run.

This study is innovative and adds to the literature in three ways. First, it is one of the first studies to empirically examine the relationship between environmental rules and a sustainable ecosystem. The influence of environmental regulations on the quality of the environment has been the subject of several studies in which this issue has been investigated experimentally [10,11,12,13]. Nevertheless, the literature lacks adequate study on the causal nexus between the mentioned variables. Second, this study considered the role of RERD, economic expansion, and TI in a sustainable environment. The contribution of previous studies has its own importance [14,15,16,17,18,19,20], but these studies lack the identification of a comprehensive causal association between the mentioned variables. The present study fills this void in the case of the U.S. Third, this study is the first to investigate the causal relationships between economic growth, technological innovation, environmental policy stringency, R&D investment in renewable energy, and carbon emissions for the U.S. Finally, wavelet coherence analysis, which is used to observe causality relationships among variables, contributes to the literature by providing us with information about causality relationships in the time and frequency domains.

3. Data, Model and Methodology

3.1. Data and Variable Description

Based on the objectives and previous studies outlined in Section 2, five variables were selected for this study. The most commonly used environmental indicator represents the sustainable environment, i.e., CO₂ emissions, which are believed to be the main indicator of environmental deprivation, and an increase in CO₂ further drives global warming and climate change [36,37,38].

All economies around the world have focused on achieving higher economic growth. In this process, these economies are rapidly expanding their industrial sector, which consumes a lot of energy and releases CO₂ and other polluting gases that affect the environmental quality. Therefore, it is relevant to consider the gross domestic product (GDP) as it could be the most important factor for CO₂ in any region. Moreover, countries with lower environmental quality pay more attention to environmental rehabilitation nowadays. Therefore, governors and policy makers are now more concerned about the stringent environmental policies to address the problem. The second exogenous variable to consider is environmental policy stringency (EPS), which is a metric that assesses the degree of stringency of environmental policy in a country. It is designed to be both country-specific and internationally applicable to allow meaningful comparisons between different countries. The concept of stringency refers to the extent to which environmental policies impose clear or implicit costs on activities that result in pollution or environmental damage. The score is derived from an assessment of the relative stringency of 13 environmental policy instruments, focusing on climate change and air pollution [39]. The inclusion of various taxes and subsidies aimed at mitigating environmental damage makes the index a more reliable measure of regulatory action, as opposed to environmental taxes.

R&D is also important for sustainable development and growth in any economy. Following the trend of environmental cleanup, a significant contribution has been reported by RE. Therefore, it is important to investigate the association of RERD with environmental conditions.

The current era is considered the most advanced era regarding technology and innovation. Still, the statement could not be established stating that TI does not impact environmental quality. Even though TI enhances the efficiency of the manufacturing sector. Therefore, the last exogenous variable considered in this study is TI. The dataset for all the mentioned variables is attained from multiple sources, covering the period from 1990 to 2020, which is the most updated dataset. Moreover, the data are extracted only for the U.S. economy, the world’s most advanced and industrialized country. Data on CO₂, GDP and TI are derived from the World Development Indicators, while EPS and RERD are collected from OECD stats.

Table 1. Data source and variable specification.

Variables	Specification	Sources
CO2	CO2 emissions (kt)	https://data.worldbank.org/country/US, accessed on 11 August 2023.
GDP	Unit in dollars, constant, 2015 prices.
TI	Patents by residents and non-residents
EPS	Environmental policy stringency an index for policy stringency in terms of environmental policies	https://stats.oecd.org/, accessed on 11 August 2023.
RERD	Investment in cleaner energy or R&D for renewable energy

contains the specifications of the variables and their respective data sources.

From the earlier mentioned and considered variables, this study created the general model below given as Equation (1):

$${\mathrm{C}\mathrm{O}}_2=f(GDP, EPS, RERD, TI)$$

(1)

where the model illustrates that $GDP, EPS, RERD \mathrm{and} TI$ is the function of environmental quality. The data are from 1990 to 2020 for the U.S.

3.2. Methodology

This study utilized a wavelet approach to identify the correlation between the selected time-varying variables: CO₂, GDP, EPS, RER&D, and TI in the U.S. between 1990 and 2020. There are still some other time-varying methods, including those proposed by Diebold and Yilmaz [40], such as the rolling-sample spillover index methodology, recursive cointegration, and conditional heteroscedasticity measures. However, the wavelet approach is more reliable, which can more accurately depict short- and long-term patterns and causalities of temporal variables. This (wavelet) method decomposes a time variable into an exact time scale, in contrast to other long-run and short-run procedures like error correction and cointegration. In addition, the wavelet method considers data differences and validation of necessary information, where the higher the probability of losing information while using other time-varying techniques. Thus, the wavelet specifies how the components of the time series fluctuate over time. This method divides the adopted time series into mother wavelet types that are scaled and shifted [41].

In an ordinary local study of the time series, the wavelet length varies independently during the period under study. The wavelet function can be compressed into the short components of the wavelet to detect oscillations with higher frequencies. The wavelet can also be stretched to a longer wavelet function to analyze volatility at a lower frequency. Additionally, whereas prolonged wavelet functions may be utilized to separate slow and stable variations (large windows), short wavelet functions are best for capturing quick changes (narrow windows). Importantly, the wavelet technique, which other approaches cannot achieve, enables efficient approximations by translating non-stationary time series issues into actual data. The previously mentioned are some of the advantageous facts regarding the selected method, allowing the current study to employ wavelet power spectrum for vulnerabilities or volatilities in CO₂, GDP, EPS, RER&D, and TI in the U.S. wavelet coherence to measure the causal relations between the variables mentioned. The adopted methodology is provided in brief in the upcoming section.

3.2.1. Continuous Wavelet

The current study employed a new wavelet method that establishes both short- and long-term time-frequency domain causalities for all variables. A wavelet is often an integral squared function with a real zero value for the mean. Moreover, the wavelet is characterized with the symbol ‘$\psi$’, and articulated below:

$${\psi }_{\mathcal{T},\mathcal{S}}\left(t\right)=\frac{1}{\sqrt{\mathcal{S}}}·\psi \left(\frac{t-\mathcal{T}}{\mathcal{S}}\right)$$

(2)

where $\frac{1}{\sqrt{\mathcal{S}}}$ in Equation (2) above is a standardized constant and indicates the unit variation present in the wavelet. Typically, the wavelet is composed of two parameters, including time or location ($\mathcal{T}$) and frequency ($\mathcal{S}$), which are essential for exact wavelet position identification in time. The parameters ($\mathcal{T}$ and $\mathcal{S}$) are largely attributed to wavelet movements and adaptable inflating variations, respectively.

The function denoted by $\psi$ exhibits oscillatory behavior along the temporal axis and can be interpreted as a wave function. The exact wavelet utilized here traces back to the Morlet wavelet family suggested by Goupillaud et al. [42] and can be expressed as in Equation (3):

$$\psi \left(t\right)={\pi }^{-\frac{1}{4}}\frac{1}{e^{i{\omega }_{0}t}}{e}^{-\frac{1}{2}{t}^2}$$

(3)

where ${\pi }^{-\frac{1}{4}}$ in the priorly mentioned Equation (2) is the standardization aspect captures the wavelet’s unit energy. Moreover, $e^{-\frac{1}{2}{t}^2}$ represents the Gaussian envelope with a unit standard deviation, and $e^{i{\omega }_{0}t}$ displays the complex sinusoid. Notably, the wavelet under discussion allows only for a finite set of time series data: $p\left(t\right)=\mathrm{1,2},\dots ,T$. As per Heisenberg’s uncertainty principle, the differentiation between scale and time localization is ambiguous. Rua and Nunes [43] suggested that the Morlet wavelet ${\omega }_0=6$ effectively measures the central occurrence as it stabilizes both scale and time localization.

3.2.2. The Continuous Wavelet Transforms

The continuous wavelet transforms $W_p\left(\mathcal{T},\mathcal{S}\right)$ estimates the temporal fluctuations or variations in a considered time series. The estimation process of $W_p\left(\mathcal{T},\mathcal{S}\right)$ Could be presented as follows:

$$W_p\left(\mathcal{T},\mathcal{S}\right)={\int }_{-\infty }^{\infty }p\left(t\right)·\frac{1}{\sqrt{\mathcal{S}}}{\psi }^{*}\left(\frac{\overline{t-\mathcal{T}}}{\mathcal{S}}\right)dt$$

(4)

where ‘*’ in the priorly mentioned equation represents the multifaceted conjugates and the $\mathcal{S}$ represents the components of the wavelet for $p\left(t\right)$ holds a higher or lower scale, which is conceivable once the acceptability condition is satisfied. In addition, if the scale is found to be lower (higher), this reveals higher (lower) fluctuations or wavelets. Based on the earlier discussion, it could be stated that the wavelet power spectrum (WPS) is pertinent in this case as it postulates supplementary amplitude and information of a specified time series. The process of WPS is available in the squared form, expressed as in Equation (5):

$${WPS}_p\left(\mathcal{T},\mathcal{S}\right)={\left|W_p(\mathcal{T},\mathcal{S})\right|}^2$$

(5)

3.2.3. Wavelet Coherence

After investigating volatility or vulnerability in each time variable via wavelet power spectrum, we further examined the causal connection between CO₂ and other variables considered. Regarding this, we applied the wavelet coherence approach. Besides numerous resemblances and dissimilarities between the wavelet coherence and other traditional causality approaches, the wavelet coherence approach allows to establish an association between two distinct time series, i.e., p(t) and q(t), within a unified domain of time-frequency. The cross-wavelet transform (CWT) could be presented for the two time series in Equation (6):

$$W_{pq}\left(\mathcal{T},\mathcal{S}\right)=W_p\left(\mathcal{T},\mathcal{S}\right)\overline{W_q\left(\mathcal{T},\mathcal{S}\right)}$$

(6)

where the priorly mentioned reveals that $W_p\left(\mathcal{T},\mathcal{S}\right)$ is the CWT for p(t) and $W_q\left(\mathcal{T},\mathcal{S}\right)$ is the CWT for q(t), while the bar is a complex conjugate. Moreover, the $W_{pq}$ (CWT) on the left side distinguishes covariance of p(t) and q(t) at a specific scale. The WPS is utilized to document the variances’ contributions to the series at every time scale. On the other hand, the cross-wavelet power is employed to determine the covariance influence in the time-frequency space. The wavelet coherence metric is capable of capturing the frequency components of both p(t) and q(t). Torrence and Compo [44] proposed the utilization of the squared version of wavelet coherence, which is mathematically represented as in Equation (7):

$$R^2\left(\mathcal{T},\mathcal{S}\right)=\frac{{\left|Z\left({\mathcal{S}}^{-1}{W}_{pq}\left(\mathcal{T},\mathcal{S}\right)\right)\right|}^2}{Z\left({\mathcal{S}}^{-1}{\left|W_p\left(\mathcal{T},\mathcal{S}\right)\right|}^2\right)Z\left({\mathcal{S}}^{-1}{\left|W_q\left(\mathcal{T},\mathcal{S}\right)\right|}^2\right)}$$

(7)

From the above Equation (7), it could be noted that $Z$ is the levelling method of time. Moreover, the value of $R^2\left(\mathcal{T},\mathcal{S}\right)$ is ranged between zero and one (0 ≤ $R^{2}s\left(\mathcal{T},\mathcal{S}\right)$ ≤ 1). However, it is important to mention that the value of $R^2\left(\mathcal{T},\mathcal{S}\right)$ approaching to zero (one) indicates the absence of (higher) association between time series p(t) and q(t). Moreover, the correlation in a wavelet coherence may be distinguished via colors displayed on the wavelet coherence graphical representation. The color on the graphic display ranges from blue to yellow-red. The blue color specifies no or weaker association between p(t) and q(t), while the yellow-red color specifies a higher or stronger connection between them.

3.2.4. Phase

$R^2\left(\mathcal{T},\mathcal{S}\right)$ distinguishes the correlation between p(t) and q(t). Still, this approach does not indicate whether the correlation between these time series is positive or negative. Therefore, the wavelet coherence phase difference is relevant, which analyzes the positive or negative correlation with lag and lead relationship in a frequency domain of time series. The wavelet coherence phase difference is obtained by following the study of Torrence and Webster [45], and expressed as in Equation (8):

$${\varphi }_{pq}\left(\mathcal{T},\mathcal{S}\right)={\tan }^{-1}\left(\frac{\mathrm{L}\left\{Z\left({\mathcal{S}}^{-1}{W}_{pq}\left(\mathcal{T},\mathcal{S}\right)\right)\right\}}{O\left\{Z\left({\mathcal{S}}^{-1}{W}_{pq}\left(\mathcal{T},\mathcal{S}\right)\right)\right\}}\right)$$

(8)

The equation above reveals that L and O are the real as well as imaginary parts of the smooth power spectrum, accordingly. Moreover, the left-hand side $({\varphi }_{pq}\left(\mathcal{T},\mathcal{S}\right)$) provides a two-dimensional graphical display, which describes the empirical outcomes of wavelet coherence.

4. Empirical Results

4.1. Descriptive Stats and Normality Test Results

The empirical inquiry component of this study is initiated by providing descriptive statistics and a normality check for each variable being examined. It is crucial to offer the data summarized when using empirical estimates. In order to offer descriptive statistics, the present study computed the time series’ mean, median, range, and standard deviation. In addition, the Jarque–Bera normality test is performed to account for both kurtosis and skewness of the data (see

Table 2. Descriptive statistics.

	CO2	GDP	EPS	RERD	TI
Mean	6.724139	13.12692	0.208470	1.022745	−0.246047
Median	6.720334	13.15632	0.113943	1.009346	−0.239830
Maximum	6.762658	13.26361	0.500602	1.438935	−0.091892
Minimum	6.683123	12.95383	−0.234083	0.638816	−0.443373
Std. Dev.	0.024124	0.095824	0.224305	0.185406	0.110309
Jarque–Bera	1.820253	2.308512	2.483735	0.437921	2.211372
Probability	0.402473	0.315292	0.288844	0.803353	0.330984

). The normal distribution of the data represents the null hypothesis of the test, which can be disproved if significant estimates are discovered at any level of 1%, 5%, or 10%. The median value is about the same as the mean, or 6.720 kt, while the mean value for CO₂ is 6.724 kt. The minimal difference range value indicates that the CO₂ are on a roughly constant trajectory. The CO₂ standard deviation, which is just 0.024, is also shown to be extremely low. Insignificant estimations are shown by the probability value of the Jarque–Bera, which supports the notion that the data on CO₂ are normally distributed. The values for the mean, median, and lower standard deviation of GDP are also all approximately the same. However, the Jarque–Bera’s nominal p-value shows that the data are normally distributed. The RERD and TI series are discovered to be ordinarily distributed, as recommended by Jarque–Bera’s p-values. TI values are found to be negative, while the mean and median RERD values are determined to be positive. The standard deviations of these variables are larger than CO₂ and GDP.

Many economic and non-economic variables do not have the properties of stationarity. Still, these variables have foremost periodic indications with instable amplitude and frequencies. Most of the traditional estimating approaches are sensitive to analyzing non-stationary series. Therefore, this study used the WPS to capture non-stationary series fluctuation patterns, namely in CO₂, GDP, EPS, RERD, and TI from 1990 to 2020 in the U.S. However, we have used the wavelet coherence technique to determine if a causal relationship exists between the variables under discussion. Based on the study’s goals, we look at the following three issues: firstly, do the variables exhibit a time-frequency dependence? Second, if so, in which way will the causation lie for them? Thirdly, is the causal relationship true over the short term, long term, or both times? Consequently, the wavelet coherence method aids in providing answers to these queries.

4.2. Results of the Wavelet Power Spectrum

The graphical depiction of the wavelet power spectrum shows the cone of effect and reveals an edge about the first five figures. The wavelet power spectrum is not relevant below this deciding edge. In order to obtain significant results, a Monte Carlo simulation has been used, represented by a black contour and indicates a 5% level of significance. Moreover, the colors differentiate between the effects, where blue corresponds to no or low vulnerabilities or disturbance, and the red color corresponds to a higher disturbance in the time series [46].

In Figure 1, Figure 2 and Figure 3, the wavelet power spectrum illustrates vulnerabilities in the CO₂, GDP, and EPC, respectively. Specifically, for CO₂, the influential cone corresponds to the significance level between 1994 and 2016. However, only one significant region is found where the significant vulnerability occurs, ranging from 2006 to 2013. Moreover, the scale of the vulnerabilities in the CO₂ is found to decrease from 1 to 3.5 in the earlier stage while from 3 to 3.5 in the latter stage. It must be mentioned that CO₂ showed significant vulnerabilities during the 2006 energy price shock and the 2009 global financial crisis. It is noted that the scale is larger in the early stage, which indicates that CO₂ is more sensitive to energy price shock. As energy prices increase, CO₂ levels reduce due to the reduction in industrial activities. Although the vulnerabilities found in CO₂ are significant, they still indicate a lower magnitude, as the green color suggests. Moreover, no significant vulnerability is found in the GDP throughout the selected time span. The blue-green color has been identified in the EPS’s wavelet power spectrum graphical display. However, no significant region is found that demonstrates disturbance of the EPS in the selected time period for the U.S. Hence, it is concluded that GDP and EPS are not vulnerable in the selected time period.

Figure 4 and Figure 5 show that the wavelet power spectrum identifies vulnerabilities in RERD and TI. Specifically, vulnerabilities have been found in only one region in each time variable. In the RERD, a significant region was found between 2006 and 2012. However, it is noted that this disturbance is greater than that of CO₂. Additionally, this vulnerability is found at a higher frequency between 0 and 3. Here, it is noteworthy that after uncertainty in the energy market prices (2006 energy prices), the U.S. has increased its renewable-energy-related R&D budget to strengthen and empower renewable energy production and consumption. Still, the vulnerabilities are only visible in the short term.

As for TI, significant vulnerabilities have been captured by the wavelet power spectrum only in the period from 2004 to 2011. The contour indicates the blue-green color; thus, the vulnerability is lower. Nevertheless, the frequency is reported to be higher, from 1 to 4 on the scale axis.

4.3. Outcomes and Discussion on the Wavelet Coherence

In Figure 6, Figure 7, Figure 8 and Figure 9, the horizontal line in the wavelet coherence graph corresponds to time, and the upright line corresponds to frequency. Higher frequency denotes smaller scale linkage, and lower frequency denotes greater scale connection, as in the wavelet power spectrum. When taking into account the time-frequency domain, wavelet coherence is comparatively more efficient estimator than the existing causality techniques currently in use.

With reference to the empirical findings of the wavelet coherence between CO₂ and GDP (Figure 6), the graphical representation displays three significant regions where the causal relation exists between the two. The first significant region is from 1994 to 1995, the second significant region is from 1996 to 2003, and the third significant region is from 2004 to 2007. However, the first and the third regions are found to correlate with CO₂ and GDP only for the short run with higher frequencies. At the same time, the second region is noted relatively for the longer term than the other two, with a higher scale value from 4.5 to 6. In all three significant regions, it is found that the arrows are traveling to the right, indicating both variables are moving in the similar direction. Moreover, the arrows were also found moving to the downright and upper right positions. This indicates a two-way causality relationship between CO₂ and development of the economy. Still, the influence of economic expansion is observed to be stronger on CO₂. The empirical outcomes are similar to the findings of Li et al. [22], which demonstrate a bidirectional causality between the two for the G20 economies. Economies boost industrial activities to attain higher economic growth. However, to run the industrial sector, they consume a higher amount of energy obtained from fossil fuels, which are emission intensive [16,18,21]. As a result, increasing CO₂ levels are a major determinant of environmental degradation and global warming.

With reference to the empirical results of the wavelet coherence between CO₂ and environmental policies (Figure 7), the wavelet coherence graphical display recognized two substantial regions where a causal relationship exists. Particularly, the 1994–1995 and 2008–2015 regions showed significant causalities between the two time series. However, in the first region, the arrows move to the right, indicating that the relationship is in phase. However, the arrows travel to the left in the second region, indicating the anti-phase association between CO₂ and EPS. The phase relationship is only present for a very short time, while the anti-phase association exists in the long run. The association in the first region holds a lower scale value of 0–1.5, while the scale value for the second region is greater, i.e., from 0.5 to 3. The arrows are found to travel to the right-up in the first region, revealing that the EPS significantly causes CO₂ but only in the shorter run. On the other hand, the arrows point to the left-up, which reveals that CO₂ significantly causes EPS relatively in a longer period than the former. The current study’s results are in agreement with the empirical work of Wolde-Rufael and Mulat-Weldemeskel [28] and Wolde-Rufael and Weldemeskel [19], demonstrating the unidirectional causality from EPS and environmental taxes to CO₂. Conversely, the causal association between environmental degradation to EPS is consistent with the earlier findings of Kongbuamai et al. [30] for BRICS economies.

With reference to the empirical findings of wavelet coherence between CO₂ and RERD (Figure 8), the graphical display unveils two regions where the causal association exists. Although the causal influence is spotted in the influential cone, it is still not up to the mark significance level as there is no contour in the graph inside the influential cone. In addition to having no contour, the arrows may be seen pointing up, upper right, upper left, and down right. This suggests that the causal relationship between the variables under consideration is bidirectional but negligible. In the long term, from 2004 to 2014, this symmetrical and negligible causal connection is observed with a greater frequency on a 0–4 scale. The findings on Influential Cone might be understood, which is similar to the prior work of Shao et al. [15], by emphatically demonstrating that a bidirectional causal relationship exists between CO₂ and R&D in the U.S., even though the causal nexus is not significant at the 5% level.

In the graphical representation with the empirical results of wavelet coherence between CO₂ and TI (Figure 9), only one significant range was found from 2004 to 2014, confirming the long-term causal relationship between them.

As shown by the dark yellow color, there is a significant causal relationship between the under-discussion variables. This causal nexus occurs more frequently (0–4). The direction of the arrows, which shows that the link between CO₂ and TI is in phase, is to the right. Additionally, the arrows show movement in a right-up direction, illuminating a one-way causal connection between TI and CO₂ release. These findings contradict earlier studies such as those by Lyu et al. [11], Ullah et al. [12], and Zhang et al. [13], which illustrate that TI significantly reduces CO₂ levels in the region. The major reason for the contradictory results is that TI in the U.S. economy is devoted only to the production and expansion function rather than the energy efficiency function. Nonetheless, this TI could lead to higher economic growth and development. TI should consider the environmental recovery factor, which will lead to a sustainable economy and environment.

5. Conclusions and Policy Recommendation

5.1. Conclusions

This study examined the relationship between environmental laws and a sustainable environment by considering economic development, RERD, and technological advancement. Using the expanded and latest dataset for the variables, spanning the U.S. from 1990 to 2020. This study aims to objectively investigate the relationship between environmental factors, environmental laws, and other exogenous variables. For this reason, the current study substituted a strict environmental policy for environmental legislation. The recent study used the groundbreaking wavelet method to achieve the desired outcome. Based on its specifications, which include enabling two time series in a collective time-frequency domain regardless of holding stationarity qualities, the wavelet approach is taken into consideration. This study employed WPS and wavelet coherence techniques, namely the wavelet method, which offers reliable estimates for both the short and long run.

The empirical results of the WPS suggest that 2006 to 2013 (CO₂), 2006 to 2012 (renewable energy R&D), and 2004 to 2011 (technical innovation) had vulnerabilities, respectively. In addition, vulnerabilities are more frequently detected in renewable energy R&D. Compared to renewable energy R&D, the vulnerabilities in CO₂ and TI are discovered less frequently. CO₂ and TI disturbances are detected substantially more frequently than renewable energy R&D. It was also discovered that the variables GDP and the rigor of environmental regulation were steady across the chosen time frame. The results show both a phase and an anti-phase link between CO₂ and other factors in the empirical research on wavelet coherence. In particular, the wavelet coherence shows that economic development and CO₂ follow the same trajectory. Additionally, there is a reciprocal causal relationship between them. However, it is discovered that economic expansion has a higher causal impact on CO₂. About EPS, the relationship is discovered during a phase in which EPS considerably increases CO₂, but only in the short term. On the other hand, a long-term anti-phase connection has been shown, where EPS is strongly caused by CO₂. As a result, a causality association between the two time series is verified in both directions. The wavelet coherence between TI and CO₂ likewise revealed a phase connection. Still, it also shows that there is a long-term, true unidirectional causality extending from TI to CO₂. However, there is no conclusive link between CO₂ and R&D in renewable energy. These results are all comparable to those from past research.

5.2. Policy Recommendation

U.S. policymakers should take a variety of actions to reduce CO₂ emissions, accompanied by evidence. In this context, increasing EPS can reduce CO₂ emissions, and the U.S. government should adopt carbon pollution standards for the industrial sector and promote the reduction in environmental degradation through strict environmental policies. The study concludes that industrial production increases CO₂ emissions during economic expansion. The Environmental Kuznets Curve (EKC) hypothesis is known to state that CO₂ emissions increase primarily as income increases, and that the relationship between CO₂ and economic development decouples when income exceeds a certain threshold. The EKC hypothesis implies that the phase in which income reduces CO₂ emissions may be associated with technological development (technique effect). In this context, the U.S. government should allocate more budget for RERD. The results of the study suggest that RERDs are not active in reducing CO₂ emissions. Although some researchers have found that RERD is effective in improving environmental quality [47], the results of this study are consistent with the statement of Pata et al. [48] that RERD is ineffective in minimizing environmental degradation. The study used wavelet transformers and considered the characteristics of the frequency domain properties in the relationship between the variables. These results suggest that U.S. policy makers should increase their investment in RERD and continue to promote their technological development in this area. For this reason, tax exemptions and favorable loans should be provided to companies engaged in renewable energy R&D activities and the development of solar cells and wind turbines. In this way, the U.S. can better achieve its CO₂ reduction targets.